y^{''}-100y=cosh(10x)

Lösung

y^{^{''}} - 100 y = cosh (10 x)

y = c_{1} e^{10 x} + c_{2} e^{- 10 x} + \frac{e ^{10 x} ( - e ^{- 20 x} + 20 x ) - e ^{- 10 x} ( 20 x + e ^{20 x} )}{800}

Schritte zur Lösung

y^{''} (x) - 100 y = cosh (10 x)

Solve linear ODE:

y = c_{1} e^{10 x} + c_{2} e^{- 10 x} + \frac{e ^{10 x} ( - e ^{- 20 x} + 20 x ) - e ^{- 10 x} ( 20 x + e ^{20 x} )}{800}

y = c_{1} e^{10 x} + c_{2} e^{- 10 x} + \frac{e ^{10 x} ( - e ^{- 20 x} + 20 x ) - e ^{- 10 x} ( 20 x + e ^{20 x} )}{800}

y^{^{''}} - y^{^{'}} + 5 y = e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x} - 5

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = 16 sin (x)

y^{^{''}} - 2 y^{^{'}} = 7 cos (3 t)

y^{^{''}} - 16 y^{^{'}} + 64 y = 504 sin (x) - 128 cos (x)